Rate of convergence of Thresholding Greedy Algorithms

2023/04/19 by Vladimir Temlyakov, Temlyakov, V. N.
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Algorithms and Data Compression #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2304.09586

openalex publication_date 2023/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The rate of convergence of the classical Thresholding Greedy Algorithm with respect to bases is studied in this paper. We bound the error of approximation by the product of both norms -- the norm of f and the A₁-norm of f. We obtain some results for greedy bases, unconditional bases, and quasi-greedy bases. In particular, we prove that our bounds for the trigonometric basis and for the Haar basis are optimal.

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